In many instances, an integrated circuit does not perform as initially designed and anticipated due to coupling capacitances. Consequently, accurate calculations of coupling capacitances play an increasingly important role in the IC design process. One reference, U.S. Pat. No. 6,931,613 issued to Kauth et al. on 16 Aug. 2005 titled “Hierarchical Feature Extraction for Electrical Interaction Calculation”, recognizes this need to accurately model the multiple capacitances between circuit elements and describes a method of calculating the electrical interactions in an integrated circuit. The referenced method recognizes that capacitances are potentially created between circuit elements due to their area and physical proximity to other each other. Also, absent an intervening element, each element in the circuit has a plate capacitance between it and the substrate, which can be modeled as a capacitor connected between the lower surface of the element and the substrate. Additionally, the vertical edges of the element create fringe capacitances between the element and the substrate, which models as a capacitor connected between one edge of the element and the substrate. Further, crossover capacitances occur between a given circuit element on one layer and another circuit element on another layer of the chip. Thus, the circuit element additionally has a crossover plate capacitance and a crossover fringe capacitance. Finally, the circuit element has a near body capacitance between it and a neighboring element on the same or different layer.
The need to accurately determine the capacitances extends beyond circuit elements and includes interconnects between elements in an integrated circuit. U.S. Pat. Application No. 2002/0116696 by Suaya et al. titled “Capacitance and Transmission Line Measurements for an Integrated Circuit” describes a method and apparatus for determining the capacitances of wires in and IC. Further, as IC designs move further into submicron and nano-scale sizes with increasing element density, the capacitance coupling effect becomes more and more significant. And, therefore, accurate modeling of these interactions becomes increasingly more important.
Also, the submicron and nano-scale drive places increasing demand on improved fabrication processes. In one such fabrication process discrete blocks of fill—typically aluminum or copper metal tiles—are added to a layer to improve planarity of the chemical-mechanical polishing process before a subsequent layer is added. The fill floats in the substrate layer and is not connected to a power supply, nor is fill physically connected to signal paths. Nevertheless, these conductive blocks of fill add unintended parasitic capacitance to the IC.
Fill material refers to the collection of individual, electrically isolated metal tiles. And, each individual fill tile, in turn, is referred to as a fill net. The fill nets are structurally and electrically different than the signal nets referred to herein. As a result of the strategic placement of fill added during fabrication, capacitance coupling occurs beyond element-to-element or signal paths (also called signal nets) and includes coupling capacitance to the floating fill nets. Yet, because this floating fill is metal, it influences the circuit performance. Specifically, the fill creates coupling capacitances with the signal nets and with other pieces of fill. And, as IC designs become increasingly dense, the capacitive coupling effects of the fill become a greater influence on IC performance.
Traditional tools for layout parameter extraction of resistances and capacitances at nodes within the IC design include CALIBRE® xRC brand extraction tool available from Mentor Graphics, and other tools available from Synopsys and Cadence, for example. These tools typically extract capacitances and resistance values and back-annotate the data to a circuit simulation that re-simulates the design to ensure the physical aspects of the design will not cause failure and to ensure it meets its function and or performance parameters. Extracting capacitances refers to a calculation determining the inherent capacitance values of a signal net based on its geometry and relationship to its environment in a particular IC design. And, extracting coupling capacitances refers to a calculation determining the capacitance values between two nets, such as two signal nets, a signal net and a fill net, or between two fill nets.
One prior-art extraction method accounts all the capacitive couplings from signal nets to fill nets and from fill nets to fill nets and is represented, for example, in FIG. 19. This prior-art approach involves an exact reduction of each interaction to precisely calculate the effective grounded capacitances and the effective coupling capacitances for the signal nets. Gaussian elimination of the fill net rows in a capacitance matrix formulation is applied. However, this method is not well-suited to every imaginable IC design because as the density and quantity of signal nets in a given area increase, and as more floating fill nets increase, the number of possible interactions grows factorially—and this creates a practical ceiling based on available computational ability of processors.
To simplify this, the entire circuit of both signal nets and floating fill nets are not represented in a single matrix. Because signal nets stop the propagation of floating fill net effects, clusters of signal nets coupled by fill nets can be represented by a simpler matrix that can be solved for the effective intrinsic and coupling capacitance. Thus, theoretically, if all the clusters of nets were small, then this simpler matrix substitution could be implemented for an accurate extraction.
This approach assumes that fill is widely spaced and stacked in layers—resulting in few inter-coupled fill nets. In reality, however, the assumption of small cluster matrix representations is not always valid. Instead, fill tiles are often spaced closely enough that they interact in a capacitive-coupled, three-dimensional mesh. Such a mesh can have hundreds of thousands of fill nets or more that would need to be eliminated in the matrix—a task that is not pragmatically solvable.
In sum, traditional extraction methods cannot be applied to the ever-increasing complexity of modern IC designs. As the number of circuit elements increase to meet market demand for smaller, more powerful IC designs, the coupling capacitance effect becomes more profound and, more importantly, the interaction effect grows factorially with the number of circuit elements. This factorial growth outpaces computational resources making this traditional method of extraction impossible. And, fabrication-improvement techniques, such as strategically placing fill material, further increases computational complexities due to coupling capacitances of fill-to-fill and fill-to-signal net interactions. Thus, the traditional method of exact extraction has reached a practical limit, and an accuracy limit.
Accordingly, there remains a need to determine the capacitance coupling effect. There is a need for an approximation method that reduces the computational complexity of coupling capacitances due to floating fill nets in an integrated circuit design. Moreover, the results of such an approximation method should enable subsequent analysis tools to optimize the IC design.